Half-space Macdonald processes

Understand

Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions.

• These measures are a useful tool to uncover the integrability of many probabilistic systems, including the Kardar-Parisi-Zhang (KPZ) equation and a number of other models in its universality class.
• In this paper we develop the structural theory behind half-space variants of these models and the corresponding half-space Macdonald processes.
• These processes are built using a Littlewood summation identity instead of the Cauchy identity, and their analysis is considerably harder than their full-space counterparts.